Some properties of monotone set functions defined by Choquet integral

In this paper, some properties of the monotone set function defined by theChoquet integral are discussed. It is shown that several important structural characteristics of theoriginal set function, such as weak null-additivity, strong order continuity, property (s) andpseudomelric generating property, etc., are preserved by the new set function. It is also shown thatC-integrability assumption is inevitable for the preservations of strong order continuous andpseudometric generating property.

Monotone Set-Valued Function Defined by Set-Valued Choquet Integral

Structural characteristics and absolute continuities of monotone set-valued function defined by set- valued Choquet integral are discussed. Similar to the single-valued monotone set function, several important structural characteristics of set-valued function are defined and have been proven the same as those in the original set functions, such as null-additivity, weakly null-additivity, order continuity, strong order continuity and property（S）. A counterexample shows that order continuity and strong order continuity of the original set functions are no longer kept in a monotone set-valued function when Choquet integrably bounded assumption is abandoned. Four kinds of absolute continuities are defined for set-valued function, and all been proven valid with respect to the original set functions.

System of set-valued mixed quasi-variational-like inclusions involving H-η-monotone operators in Banach spaces

A new system of the set-valued mixed quasi-variational-like inclusions （SSMQVLI） involving H-η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolvent operator technique of H-η-monotone operators, a new iterative algorithm for finding approximate solutions to SSMQVLI is proposed. It is shown that the iterative sequences generated by the algorithm converge strongly to the exact solution of SSMQVLI under appropriate assumptions. These obtained new results have extended and improved previous results.

单调集值测度空间上函数列的伪依测度收敛

在单调集值测度空间上,首先给出了函数列伪依测度收敛与伪几乎处处收敛的一个关系,然后研究了单调集值测度在一致伪自连续的条件下,函数列伪依测度收敛的几个性质.

多尺度决策系统中测试代价敏感的属性与尺度同步选择

属性与尺度同步选择方法可有效解决涉及代价因素的多尺度决策系统的知识约简问题,然而在现有研究中,少有基于代价进行属性与尺度的同步选择,并且大多数算法只针对协调的多尺度决策系统或不协调的多尺度决策系统.为了解决这一问题,文中以最小化数据处理的总测试代价为目标,提出测试代价敏感的属性与尺度同步选择算法,同时适用于协调的多尺度决策系统和不协调的多尺度决策系统.首先,构造基于粗糙集的理论模型,模型中的概念及性质同时考虑属性因素和尺度因素.其次,基于粗糙集的理论模型,设计启发式算法,能基于测试代价对多尺度决策系统同时进行属性约简与尺度选择,并且不同的属性可选择不同的尺度.最后,在12个数据集上的实验验证文中算法的有效性、实用性及优越性.

One-dimensional monotone nonautonomous dynamical systems

This work is devoted to the study of the dynamics of one-dimensional monotone nonautonomous(cocycle) dynamical systems. A description of the structures of their invariant sets, omega limit sets,Bohr/Levitan almost periodic and almost automorphic motions, global attractors, and pinched and minimalsets is given. An application of our general results is given to scalar differential and difference equations.

单调回复关系中稳定的Farey相邻元与拓扑熵

论文旨在利用数论中的Farey相邻元研究高维柱面扭转映射系统的复杂性。鉴于单调回复关系的解和高维柱面扭转映射的轨道之间存在一一对应的关系,问题转化为研究单调回复关系解系统的复杂性。假定单调回复关系的旋转集中有一对稳定的Farey相邻元p/q和p′/q′,利用周期延拓的方法,构造一对交换旋转数p/q和p′/q′的上下解,进而根据Angenent判据,得到系统具有正拓扑熵的结论。

A Simple Method to Derive Minimal Cut Sets for a Non-coherent Fault Tree

Minimal cut sets （or prime implicants： minimal combinations of basic event conditions leading to system failure） are important information for reliability/safety analysis and design. To obtain minimal cut sets for general non-coherent fault trees, including negative basic events or multi-valued basic events, a special procedure such as the consensus rule must be applied to the results obtained by logical operations for coherent fault trees, which will require more steps and time. This paper proposes a simple method for a non-coherent fault tree, whose top event is represented as an AND combination of monotonic sub-trees. A ＂monotonic＂ sub-tree means that it does not have both positive and negative representations for each basic event. It is proven that minimal cut sets can be obtained by a conventional method for coherent fault trees. An illustrative example of a simple event tree analysis shows the detail and characteristics of the proposed method.

Dominance-based rough set approach as a paradigm of knowledge discovery and granular computing

Dominance-based rough set approach(DRSA) permits representation and analysis of all phenomena involving monotonicity relationship between some measures or perceptions.DRSA has also some merits within granular computing,as it extends the paradigm of granular computing to ordered data,specifies a syntax and modality of information granules which are appropriate for dealing with ordered data,and enables computing with words and reasoning about ordered data.Granular computing with ordered data is a very general paradigm,because other modalities of information constraints,such as veristic,possibilistic and probabilistic modalities,have also to deal with ordered value sets(with qualifiers relative to grades of truth,possibility and probability),which gives DRSA a large area of applications.

Set-Valued Non-Linear Random Implicit Quasivariational Inclusions

In this paper, we propose iterative algorithms for set valued nonlinear random implicit quasivariational inclusions. We define the related random implicit proximal operator equations and establish an equivalence between them. Finally, we prove the existence and convergence of random iterative sequences generated by random iterative algorithms.

EFFICIENT NONNEGATIVE MATRIX FACTORIZATION VIA MODIFIED MONOTONE BARZILAI-BORWEIN METHOD WITH ADAPTIVE STEP SIZES STRATEGY

In this paper,we develop an active set identification technique.By means of the active set technique,we present an active set adaptive monotone projected Barzilai-Borwein method(ASAMPBB)for solving nonnegative matrix factorization(NMF)based on the alternating nonnegative least squares framework,in which the Barzilai-Borwein(BB)step sizes can be adaptively picked to get meaningful convergence rate improvements.To get optimal step size,we take into account of the curvature information.In addition,the larger step size technique is exploited to accelerate convergence of the proposed method.The global convergence of the proposed method is analysed under mild assumption.Finally,the results of the numerical experiments on both synthetic and real-world datasets show that the proposed method is effective.

基于代数观点的邻域区间集粗糙集模型研究

描述部分已知概念的区间集粗糙集是对经典粗糙集的拓展,其属性值概念由上下边界集来描述,具有较好的不确定性刻画能力,能够有效促进数据挖掘、信息度量和知识发现等实际应用。现有研究主要针对离散型数据对象,不能很好地处理现实世界中大量存在的连续型数据对象,因此区间集粗糙集具有改进的空间。该文引入邻域关系,通过Hausdorff距离函数定义区间集邻域粒子,由此构造邻域区间集粗糙集模型,并从代数观点研究其相关概念及性质,最后用实例分析验证其有效性。

区间上的单调函数的连续性及其广义反函数

利用勒贝格测度理论证明了区间上的单调函数几乎处处连续,利用商集理论定义了一种带有参数的广义反函数,证明其与原函数具有相同的单调性。在此基础上,证明了广义反函数的广义反函数几乎处处等于原函数,并给出了实例加以印证。

量化粗糙集的单调性属性约简方法

单调性在经典粗糙集属性约简过程中发挥着重要的作用。然而,在一些泛化模型(如量化粗糙集模型)中该性质并不存在。针对该问题,提出了量化粗糙集模型中下近似单调约简的定义,并给出了求得该约简的启发式方法。实验结果表明,相较于下近似保持约简算法,下近似单调约简算法不仅耗时短,而且增加了由正域和边界域表示的确定性,同时降低了由边界域带来的不确定性。

求平面点集凸壳的一种新算法

在研究了大量的求平面点集凸包的算法基础上,提出了一种新的构造平面点集的凸壳算法。此算法先求出四个极值点,构造出一个四边形。对于四边形外面的点依次用二分法进行判断是属于哪个线段区域;对于一个线段区域上的点只需要找出右侧的点,分别和线段的两个端点连接得到新的多边形链,依次这样处理每个点,直到结束。这样就得到四个简单多边形单调链,然后对单调链求凸点,时间复杂度为O(n),最后求得的每个凸点就是平面点集的凸壳,此算法总的时间复杂度不超过O(nlogn)。

二型模糊集下的推理模型及Mamdani推理算法

在二型模糊集理论的基础上,讨论了二型模糊集下的三种模糊推理模型,研究了模糊推理模型的Mamdani推理算法,证明了Mamdani推理算法具有单调性质。

决策粗糙集的属性约简准则研究

属性约简是粗糙集理论研究的重要内容之一.在传统Pawlak粗糙集模型中,随着属性数量的单调变化,下、上近似集也单调变化.然而,在决策粗糙集模型中,随着属性的单调增加,下、上近似集有可能增加也有可能减少.针对这一问题,从优化角度给出了决策单调准则、一般性准则和代价准则的适应性函数并通过遗传算法求得三种准则下的约简.实验结果表明:决策单调准则约简获得了更多的正域规则;一般性准则约简获取了最多的正域规则;代价准则约简获得了最小的决策代价.

简单多边形集凸包的快速算法

提出了一个简单多边形集凸包的快速算法。先求出每个简单多边形的(子)凸包,根据凸包的切线性质,从有关的子凸包中抽取一段严格单调的折线。应用归并排序方法把位于一条直线右侧的一组严格单调的折线合并成一条折线,把合并后的折线和子凸包集的外接矩形上的边连结成一条封闭折线,即一个简单多边形,使其能够把所有子凸包包围起来,最后求出这个简单多边形的凸包。算法的时间复杂度为线性O(n),并且给出一个例子进行了验证。

决策粗糙集属性约简:一种局部视角方法

比较于经典粗糙集,决策粗糙集模型将代价问题考虑在内,为粗糙集的属性约简问题带来了新的挑战。尽管已有针对决策粗糙集的一些属性约简方法被提出,但这些约简标准都是基于所有决策类的,约束条件较为严格。为解决这一问题,从局部视角出发,针对单独的决策类提出了Local约简的思想。基于启发式算法求解约简的实验结果表明,相比于面向所有决策类的约简,Local约简可以获得更多的正域规则,同时也能够进一步降低约简中的属性数量。